Such admissible sets are well-understood and widely used in the context of
effective properties of composite materials
[1]}, [2]}, [3]}, [4]}, [5]}. Our analysis is inspired by the
one in [6]} and reaches somewhat similar conclusions. However, it is
based on Theorem REF  rather than the explicit representation of
Stieltjes functions from Theorem REF , used in prior work.
The question of bounds on values of Stieltjes functions in the case when the
spectral measure \(\sigma \)  is known in an interval of frequencies is addressed in
[7]}. The bounds in the case when the phase of the analytic function
is known on a part of the boundary, and on the modulus on the remaining part
have been derived in [8]} by means of a modified Nevanlinna-Pick problem.
